Problem: What is the value of the following logarithm? $\log_{100} 10$
Explanation: If $b^y = x$ , then $\log_{b} x = y$ Notice that $10$ is the square root of $100$ That is, $\sqrt{100} = 100^{1/2} = 10$ Thus, $\log_{100} 10 = \dfrac{1}{2}$.